Surely the dead in 'dead heat' does mean 'no longer alive' rather than exact. A heat is a preliminary round in a competition, designed to decide who meets who in later rounds (or heats). If two contestants finish at the same time, or with the same number of points in a heat, then it hasn't decided anything and may just as well not have happened, so it is a 'dead' heat. I don't have any references to back this up, it's just an opinion.